DOC PREVIEW
U-M CHEM 451 - Steady-State Approximation to Rate Law
Type Lecture Note
Pages 6

This preview shows page 1-2 out of 6 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

From Steady-State Approximation to Rate LawTemperature dependence of the reaction rate constantMaxwell-Boltzmann theoryThe Arrhenius EquationTypical activation energiesApplying our knowledge to enzymes: Invertase (β-fructofuranosidase)Michaelis-MentenCHEM 451 1st Edition Lecture 6Outline of Last Lecture I. Rate constanta. StoichiometryII. Rate Lawsa. Half LifeIII. Elementary Reaction StepsOutline of Current Lecture IV. From steady-state approximation to rate lawV. Connection between Kinetics and ThermodynamicsVI. Temperature dependence of the reaction rate constanta. Maxwell-Boltzmann Theoryb. The Arrhenius Equationc. Typical activation energiesVII. Applying our knowledge to enzymes: InvertaseVIII. Michaelis-MentenCurrent LectureFrom Steady-State Approximation to Rate Lawd[N2O2]dt=k1[NO]2−d[N2O2]dt=k−1[NO]2−d[N2O2]dt=k2[N2O2] [O2]Σ=d[N2O2]dt=k1[NO]2−k−1[NO]2−k2[N2O2] [O2]=0This is known as the steady state approximation. [N2O2] remains small and constant throughout.[N2O2]=k1[NO]2k−1[NO]2+k2[O2]∧d[NO2]dt=2 k2[N2O2] [O2]These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.d[NO2]dt=2 k1k2[NO]2[O2]k−1[NO]2+k2[O2]∧k−1≫ k2N2O2 either falls apart or becomes a product; rapidly decaying.Reaching Equilibrium: Connection between Kinetics and ThermodynamicsThe reversible reaction has 2 elementary steps: production of B and decay of B to A.d[B]dt=k1[A]−k−1[B]If you plot the concentrations of A and B over time, you will see that they reach dynamic equilibrium.Dynamic Equilibrium – individual molecules are producing product at the same rate as they are decaying. Overall [A] and [B] do not change.This gives rise to the thermodynamic equilibrium constant K.K=k1k−1=[B]eq[A]eqTemperature dependence of the reaction rate constantMaxwell-Boltzmann theory- If molecules exceed a threshold (critical velocity); they have sufficient energy to react into product.- Temperature dependence: increased temperature increases overall kinetic energy, thus increasing the number of molecules that exceed threshold.o This increases the rate of acceleration- Activation Energy (Ea): The minimum energy that must be supplied by a collision as Ea= ½ mv2 per mole reaction.- The rate constant is dependent on A∞ or the pre-exponential factor: the maximal rate constant if infinite energy (infinite temperature) were available and an instantaneous reaction could occur.- Rule of thumb: A 10 0C increase will double the rate.- NOTE: do not confuse with enzymes, which lower the activation energy barrier so that more molecules can react spontaneously at the same temperature.The Arrhenius EquationThis will give you a linear function if you plot lnk vs. 1/T. The slope will be –Ea/R.Typical activation energies- Reaction coordinate Q tells us the position in the reaction.- Exothermic reactions have a small activation energy and large thermodynamic gain. Theywill occur rapidly if Ea<RT and slowly if Ea>>RT- Endothermic reactions will normally have a large activation energy, which is required to get to a higher energy product.Applying our knowledge to enzymes: Invertase (β-fructofuranosidase)- Enzymes are heterogenous catalysts. They bind substrate on the surface of the enzyme.- Invertase: hydrolyzes sucrose into fructose and glucose.o This leads to a change in the chiral property of the solutiono Optical properties are measured via polarized light.- Pre-steady state: product needs time to build up because the [ES] complex needs to form first.- Steady state: reached once [ES] is stable (unchanging)- Eventually, equilibrium is reached where the formation of product and degradation to substrate are at a constant rate.- When the sucrose concentration is much higher than that of the enzyme, the reaction ratebecomes independent of the sucrose concentration (zero order with respect to sucrose).- He therefore proposed that the overall reaction is composed of two elementary reactions in which the substrate forms a complex with the enzyme that subsequently decomposes to products and enzyme. Michaelis-MentenE+S k1→ES k2→P+EWhen the substrate concentration becomes high enough to entirely convert the enzyme to the ES form, the second step of the reaction becomes rate limiting and overall reaction ratebecomes insensitive to further increases in substrate concentration.v =d[P]dt=k2[ES]The overall rate of production of the enzyme-substrate complex is the difference between production and decay.d[ES]dt=k1[E] [S]−k−1[ES]−k2[ES]There are two assumptions we make here.1. Fast equilibrium: k-1>>k2. ES is in equilibrium with E + S.2. Steady state: After [ES] builds up, it becomes steady because the amount lost = amount remade.[E]T = [E] + [ES]Now, we work some algebra….d[ES]dt=k1[E] [S]−k−1[ES]−k2[ES]=0[E]=[E]T−[ES]k1([E]T−[ES])[S]=(k−1+k2)[ES][ES](k−1+k2+k1[S])=k1[E]T[S][ES]=[E]T[E]KM+[S], where KM=k−1+k2k1The initial velocity is the velocity measured before more than 10% of the substrate has been converted to product.v0=d[P]dt=k2[ES]=k2[E]T[S]KM+[S]The maximal velocity (Vmax) occurs at high substrate concentrations when the enzyme is saturated (entirely in ES form)Vmax=k2[E]TSome more


View Full Document

U-M CHEM 451 - Steady-State Approximation to Rate Law

Type: Lecture Note
Pages: 6
Download Steady-State Approximation to Rate Law
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Steady-State Approximation to Rate Law and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Steady-State Approximation to Rate Law 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?